IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v90y2022i3p551-562.html
   My bibliography  Save this article

Should We Condition on the Number of Points When Modelling Spatial Point Patterns?

Author

Listed:
  • Jesper Møller
  • Ninna Vihrs

Abstract

We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice because most point pattern data consist of only one pattern. We therefore explore the possibility to condition on the number of points instead when fitting and validating spatial point process models. In a simulation study with different popular spatial point process models, we consider model validation using global envelope tests based on functional summary statistics. We find that conditioning on the number of points will for some functional summary statistics lead to more narrow envelopes and thus stronger tests and that it can also be useful for correcting for some conservativeness in the tests when testing composite hypothesis. However, for other functional summary statistics, it makes little or no difference to condition on the number of points. When estimating parameters in popular spatial point process models, we conclude that for mathematical and computational reasons, it is convenient to assume a distribution for the number of points.

Suggested Citation

  • Jesper Møller & Ninna Vihrs, 2022. "Should We Condition on the Number of Points When Modelling Spatial Point Patterns?," International Statistical Review, International Statistical Institute, vol. 90(3), pages 551-562, December.
    • Handle: RePEc:bla:istatr:v:90:y:2022:i:3:p:551-562
    DOI: 10.1111/insr.12501
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12501
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12501?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Frédéric Lavancier & Jesper Møller & Ege Rubak, 2015. "Determinantal point process models and statistical inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 853-877, September.
    3. Adrian Baddeley & Jean-François Coeurjolly & Ege Rubak & Rasmus Waagepetersen, 2014. "Logistic regression for spatial Gibbs point processes," Biometrika, Biometrika Trust, vol. 101(2), pages 377-392.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jesper Møller & Heidi S. Christensen & Francisco Cuevas-Pacheco & Andreas D. Christoffersen, 2021. "Structured Space-Sphere Point Processes and K-Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 569-591, June.
    2. José J. Quinlan & Fernando A. Quintana & Garritt L. Page, 2021. "On a class of repulsive mixture models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 445-461, June.
    3. Kateřina Koňasová & Jiří Dvořák, 2021. "Stochastic Reconstruction for Inhomogeneous Point Patterns," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 527-547, June.
    4. Tomáš Mrkvička & Tomáš Roskovec & Michael Rost, 2021. "A Nonparametric Graphical Tests of Significance in Functional GLM," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 593-612, June.
    5. Johan Debayle & Vesna Gotovac Ðogaš & Kateřina Helisová & Jakub Staněk & Markéta Zikmundová, 2021. "Assessing Similarity of Random sets via Skeletons," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 471-490, June.
    6. Jiří Dvořák & Tomáš Mrkvička, 2022. "Graphical tests of independence for general distributions," Computational Statistics, Springer, vol. 37(2), pages 671-699, April.
    7. Dai, Wenlin & Genton, Marc G., 2019. "Directional outlyingness for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 50-65.
    8. Adil Yazigi & Antti Penttinen & Anna-Kaisa Ylitalo & Matti Maltamo & Petteri Packalen & Lauri Mehtätalo, 2022. "Modeling Forest Tree Data Using Sequential Spatial Point Processes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 88-108, March.
    9. Veronika Římalová & Alessandra Menafoglio & Alessia Pini & Vilém Pechanec & Eva Fišerová, 2020. "A permutation approach to the analysis of spatiotemporal geochemical data in the presence of heteroscedasticity," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.
    10. Chaiban, Celia & Biscio, Christophe & Thanapongtharm, Weerapong & Tildesley, Michael & Xiao, Xiangming & Robinson, Timothy P. & Vanwambeke, Sophie O. & Gilbert, Marius, 2019. "Point pattern simulation modelling of extensive and intensive chicken farming in Thailand: Accounting for clustering and landscape characteristics," Agricultural Systems, Elsevier, vol. 173(C), pages 335-344.
    11. Ondřej Šedivý & Antti Penttinen, 2014. "Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 225-249, August.
    12. Jiří Dvořák & Tomáš Mrkvička & Jorge Mateu & Jonatan A. González, 2022. "Nonparametric Testing of the Dependence Structure Among Points–Marks–Covariates in Spatial Point Patterns," International Statistical Review, International Statistical Institute, vol. 90(3), pages 592-621, December.
    13. Jakob G. Rasmussen & Heidi S. Christensen, 2021. "Point Processes on Directed Linear Networks," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 647-667, June.
    14. Ghorbani, Mohammad & Vafaei, Nafiseh & Dvořák, Jiří & Myllymäki, Mari, 2021. "Testing the first-order separability hypothesis for spatio-temporal point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    15. Christophe Ange Napoléon Biscio & Frédéric Lavancier, 2017. "Contrast Estimation for Parametric Stationary Determinantal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 204-229, March.
    16. Poinas, Arnaud, 2019. "A bound of the β-mixing coefficient for point processes in terms of their intensity functions," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 88-93.
    17. Frédéric Lavancier & Jesper Møller, 2016. "Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 587-609, June.
    18. José Ulises Márquez Urbina & Graciela González Farías & L Leticia Ramírez Ramírez & D Iván Rodríguez González, 2022. "A multi-source global-local model for epidemic management," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-26, January.
    19. Ian Flint & Nicolas Privault, 2021. "Computation of Coverage Probabilities in a Spherical Germ-Grain Model," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 491-502, June.
    20. Dai, Wenlin & Mrkvička, Tomáš & Sun, Ying & Genton, Marc G., 2020. "Functional outlier detection and taxonomy by sequential transformations," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:istatr:v:90:y:2022:i:3:p:551-562. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.